Geodesic
Normalization flow in the presence of a~resonance
Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 172-195

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Following [18], we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike [18] we do not assume that frequences of the linearized system are non-resonant. We study analytic properties of the normalization procedure. In particular, we show that in the case of a codimension one resonance an analytic Hamiltonian function may be reduced to a normal form up to an exponentially small reminder with explicit estimates of the reminder and the analyticity domain.
Keywords: Hamiltonian normal forms, Hamiltonian perturbation theory. 
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D. V. Treschev. Normalization flow in the presence of a~resonance. Izvestiya. Mathematics , Tome 89 (2025) no. 1, pp. 172-195. http://geodesic.mathdoc.fr/item/IM2_2025_89_1_a7/